Controlled fusion in a field reversed configuration and direct energy conversion

ABSTRACT

A system and apparatus for controlled fusion in a field reversed configuration (FRC) magnetic topology and conversion of fusion product energies directly to electric power. Preferably, plasma ions are magnetically confined in the FRC while plasma electrons are electrostatically confined in a deep energy well, created by tuning an externally applied magnetic field. In this configuration, ions and electrons may have adequate density and temperature so that upon collisions they are fused together by the nuclear force, thus forming fusion products that emerge in the form of an annular beam. Energy is removed from the fusion product ions as they spiral past electrodes of an inverse cyclotron converter. Advantageously, the fusion fuel plasmas that can be used with the present confinement and energy conversion system include advanced (aneutronic) fuels.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.10/406,086, filed Apr. 2, 2003, which is a continuation of U.S.application Ser. No. 10/076,793, filed Feb. 14, 2002, now U.S. Pat. No.6,611,106, which claims the benefit of U.S. provisional application Ser.No. 60/277,374, filed Mar. 19, 2001, and U.S. provisional applicationSer. No. 60/297,086, filed on Jun. 8, 2001, which applications are fullyincorporated herein by reference.

FIELD OF THE INVENTION

The invention relates generally to the field of plasma physics, and, inparticular, to methods and apparati for confining plasma to enablenuclear fusion and for converting energy from fusion products intoelectricity.

BACKGROUND OF THE INVENTION

Fusion is the process by which two light nuclei combine to form aheavier one. The fusion process releases a tremendous amount of energyin the form of fast moving particles. Because atomic nuclei arepositively charged—due to the protons contained therein—there is arepulsive electrostatic, or Coulomb, force between them. For two nucleito fuse, this repulsive barrier must be overcome, which occurs when twonuclei are brought close enough together where the short-range nuclearforces become strong enough to overcome the Coulomb force and fuse thenuclei. The energy necessary for the nuclei to overcome the Coulombbarrier is provided by their thermal energies, which must be very high.For example, the fusion rate can be appreciable if the temperature is atleast of the order of 10⁴ eV—corresponding roughly to 100 milliondegrees Kelvin. The rate of a fusion reaction is a function of thetemperature, and it is characterized by a quantity called reactivity.The reactivity of a D-T reaction, for example, has a broad peak between30 keV and 100 keV.

Typical fusion reactions include:

D+D→He³(0.8 MeV)+n(2.5 MeV),

D+T→α(3.6 MeV)+n(14.1 MeV),

D+He³→α(3.7 MeV)+p(14.7 MeV), and

p+B¹¹→3α(8.7 MeV),

where D indicates deuterium, T indicates tritium, a indicates a heliumnucleus, n indicates a neutron, p indicates a proton, He indicateshelium, and B¹¹ indicates Boron-11. The numbers in parentheses in eachequation indicate the kinetic energy of the fusion products.

The first two reactions listed above—the D-D and D-T reactions—areneutronic, which means that most of the energy of their fusion productsis carried by fast neutrons. The disadvantages of neutronic reactionsare that (1) the flux of fast neutrons creates many problems, includingstructural damage of the reactor walls and high levels of radioactivityfor most construction materials; and (2) the energy of fast neutrons iscollected by converting their thermal energy to electric energy, whichis very inefficient (less than 30%). The advantages of neutronicreactions are that (1) their reactivity peaks at a relatively lowtemperature; and (2) their losses due to radiation are relatively lowbecause the atomic numbers of deuterium and tritium are 1.

The reactants in the other two equations—D-He³ and p-B¹¹—are calledadvanced fuels. Instead of producing fast neutrons, as in the neutronicreactions, their fusion products are charged particles. One advantage ofthe advanced fuels is that they create much fewer neutrons and thereforesuffer less from the disadvantages associated with them. In the case ofD-He³, some fast neutrons are produced by secondary reactions, but theseneutrons account for only about 10 percent of the energy of the fusionproducts. The p-B¹¹ reaction is free of fast neutrons, although it doesproduce some slow neutrons that result from secondary reactions butcreate much fewer problems. Another advantage of the advanced fuels isthat their fusion products comprise charged particles whose kineticenergy may be directly convertible to electricity. With an appropriatedirect energy conversion process, the energy of advanced fuel fusionproducts may be collected with a high efficiency, possibly in excess of90 percent.

The advanced fuels have disadvantages, too. For example, the atomicnumbers of the advanced fuels are higher (2 for He³ and 5 for B¹¹).Therefore, their radiation losses are greater than in the neutronicreactions. Also, it is much more difficult to cause the advanced fuelsto fuse. Their peak reactivities occur at much higher temperatures anddo not reach as high as the reactivity for D-T. Causing a fusionreaction with the advanced fuels thus requires that they be brought to ahigher energy state where their reactivity is significant. Accordingly,the advanced fuels must be contained for a longer time period whereinthey can be brought to appropriate fusion conditions.

The containment time for a plasma is Δt=r²/D, where r is a minimumplasma dimension and D is a diffusion coefficient. The classical valueof the diffusion coefficient is D_(c)=a_(i) ²/τ_(ie), where a_(i) is theion gyroradius and τ_(ie) is the ion-electron collision time. Diffusionaccording to the classical diffusion coefficient is called classicaltransport. The Bohm diffusion coefficient, attributed toshort-wavelength instabilities, is D_(B)=( 1/16)a_(i) ²Ω_(i), whereΩ_(i) is the ion gyrofrequency. Diffusion according to this relationshipis called anomalous transport. For fusion conditions, D_(B)/D_(c)=(1/16)Ω_(i)τ_(ie)≅10⁸, anomalous transport results in a much shortercontainment time than does classical transport. This relation determineshow large a plasma must be in a fusion reactor, by the requirement thatthe containment time for a given amount of plasma must be longer thanthe time for the plasma to have a nuclear fusion reaction. Therefore,classical transport condition is more desirable in a fusion reactor,allowing for smaller initial plasmas.

In early experiments with toroidal confinement of plasma, a containmenttime of Δt≅r²/D_(B) was observed. Progress in the last 40 years hasincreased the containment time to Δt≅1000 r²/D_(B). One existing fusionreactor concept is the Tokamak. The magnetic field of a Tokamak 68 and atypical particle orbit 66 are illustrated in FIG. 5. For the past 30years, fusion efforts have been focussed on the Tokamak reactor using aD-T fuel. These efforts have culminated in the InternationalThermonuclear Experimental Reactor (ITER), illustrated in FIG. 7. Recentexperiments with Tokamaks suggest that classical transport, Δt≅r²/D_(c),is possible, in which case the minimum plasma dimension can be reducedfrom meters to centimeters. These experiments involved the injection ofenergetic beams (50 to 100 keV), to heat the plasma to temperatures of10 to 30 keV. See W. Heidbrink & G. J. Sadler, 34 Nuclear Fusion 535(1994). The energetic beam ions in these experiments were observed toslow down and diffuse classically while the thermal plasma continued todiffuse anomalously fast. The reason for this is that the energetic beamions have a large gyroradius and, as such, are insensitive tofluctuations with wavelengths shorter than the ion gyroradius (λ<a_(i)).The short-wavelength fluctuations tend to average over a cycle and thuscancel. Electrons, however, have a much smaller gyroradius, so theyrespond to the fluctuations and transport anomalously.

Because of anomalous transport, the minimum dimension of the plasma mustbe at least 2.8 meters. Due to this dimension, the ITER was created 30meters high and 30 meters in diameter. This is the smallest D-TTokamak-type reactor that is feasible. For advanced fuels, such as D-He³and p-B¹¹, the Tokamak-type reactor would have to be much larger becausethe time for a fuel ion to have a nuclear reaction is much longer. ATokamak reactor using D-T fuel has the additional problem that most ofthe energy of the fusion products energy is carried by 14 MeV neutrons,which cause radiation damage and induce reactivity in almost allconstruction materials due to the neutron flux. In addition, theconversion of their energy into electricity must be by a thermalprocess, which is not more than 30% efficient.

Another proposed reactor configuration is a colliding beam reactor. In acolliding beam reactor, a background plasma is bombarded by beams ofions. The beams comprise ions with an energy that is much larger thanthe thermal plasma. Producing useful fusion reactions in this type ofreactor has been infeasible because the background plasma slows down theion beams. Various proposals have been made to reduce this problem andmaximize the number of nuclear reactions.

For example, U.S. Pat. No. 4,065,351 to Jassby et al. discloses a methodof producing counterstreaming colliding beams of deuterons and tritonsin a toroidal confinement system. In U.S. Pat. No. 4,057,462 to Jassbyet al., electromagnetic energy is injected to counteract the effects ofbulk equilibrium plasma drag on one of the ion species. The toroidalconfinement system is identified as a Tokamak. In U.S. Pat. No.4,894,199 to Rostoker, beams of deuterium and tritium are injected andtrapped with the same average velocity in a Tokamak, mirror, or fieldreversed configuration. There is a low density cool background plasmafor the sole purpose of trapping the beams. The beams react because theyhave a high temperature, and slowing down is mainly caused by electronsthat accompany the injected ions. The electrons are heated by the ionsin which case the slowing down is minimal.

In none of these devices, however, does an equilibrium electric fieldplay any part. Further, there is no attempt to reduce, or even consider,anomalous transport.

Other patents consider electrostatic confinement of ions and, in somecases, magnetic confinement of electrons. These include U.S. Pat. No.3,258,402 to Farnsworth and U.S. Pat. No. 3,386,883 to Farnsworth, whichdisclose electrostatic confinement of ions and inertial confinement ofelectrons; U.S. Pat. No. 3,530,036 to Hirsch et al. and U.S. Pat. No.3,530,497 to Hirsch et al. are similar to Farnsworth; U.S. Pat. No.4,233,537 to Limpaecher, which discloses electrostatic confinement ofions and magnetic confinement of electrons with multi-pole cuspreflecting walls; and U.S. Pat. No. 4,826,646 to Bussard, which issimilar to Limpaecher and involves point cusps. None of these patentsconsider electrostatic confinement of electrons and magnetic confinementof ions. Although there have been many research projects onelectrostatic confinement of ions, none of them have succeeded in.establishing the required electrostatic fields when the ions have therequired density for a fusion reactor. Lastly, none of the patents citedabove discuss a field reversed configuration magnetic topology.

The field reversed configuration (FRC) was discovered accidentallyaround 1960 at the Naval Research Laboratory during theta pinchexperiments. A typical FRC topology, wherein the internal magnetic fieldreverses direction, is illustrated in FIG. 8 and FIG. 10, and particleorbits in a FRC are shown in FIG. 11 and FIG. 14. Regarding the FRC,many research programs have been supported in the United States andJapan. There is a comprehensive review paper on the theory andexperiments of FRC research from 1960-1988. See M. Tuszewski, 28 NuclearFusion 2033, (1988). A white paper on FRC development describes theresearch in 1996 and recommendations for future research. See L. C.Steinhauer et al., 30 Fusion Technology 116 (1996). To this date, in FRCexperiments the FRC has been formed with the theta pinch method. Aconsequence of this formation method is that the ions and electrons eachcarry half the current, which results in a negligible electrostaticfield in the plasma and no electrostatic confinement. The ions andelectrons in these FRCs were contained magnetically. In almost all FRCexperiments, anomalous transport has been assumed. See, e.g., Tuszewski,beginning of section 1.5.2, at page 2072.

Thus, it is desirable to provide a fusion system having a containmentsystem that tends to substantially reduce or eliminate anomaloustransport of ions and electrons and an energy conversion system thatconverts the energy of fusion products to electricity with highefficiency.

SUMMARY OF THE INVENTION

The present invention is directed to a system that facilitatescontrolled fusion in a magnetic field having a field-reversed topologyand the direct conversion of fusion product energies to electric power.The system, referred to herein as a plasma-electric power generation(PEG) system, preferably includes a fusion reactor having a containmentsystem that tends to substantially reduce or eliminate anomaloustransport of ions and electrons. In addition, the PEG system includes anenergy conversion system coupled to the reactor that directly convertsfusion product energies to electricity with high efficiency.

In one innovative aspect of the present invention, anomalous transportfor both ions and electrons tends to be substantially reduced oreliminated. The anomalous transport of ions tends to be avoided bymagnetically confining the ions in a magnetic field of field reversedconfiguration (FRC). For electrons, the anomalous transport of energy isavoided by tuning an externally applied magnetic field to develop astrong electric field, which confines the electrons electrostatically ina deep potential well. As a result, fusion fuel plasmas that can be usedwith the present confinement apparatus and process are not limited toneutronic fuels, but also advantageously include advanced or aneutronicfuels. For aneutronic fuels, fusion reaction energy is almost entirelyin the form of charged particles, i.e., energetic ions, that can bemanipulated in a magnetic field and, depending on the fuel, cause littleor no radioactivity.

In another innovative aspect of the present invention, a direct energyconversion system is used to convert the kinetic energy of the fusionproducts directly into electric power by slowing down the chargedparticles through an electromagnetic field. Advantageously, the directenergy conversion system of the present invention has the efficiencies,particle-energy tolerances and electronic ability to convert thefrequency and phase of the fusion output power of about 5 MHz to matchthe frequency of an external 60 Hertz power grid.

In a preferred embodiment, the fusion reactor's plasma containmentsystem comprises a chamber, a magnetic field generator for applying amagnetic field in a direction substantially along a principle axis, andan annular plasma layer that comprises a circulating beam of ions. Ionsof the annular plasma beam layer are substantially contained within thechamber magnetically in orbits and the electrons are substantiallycontained in an electrostatic energy well. In one aspect of onepreferred embodiment a magnetic field generator comprises a currentcoil. Preferably, the system further comprises mirror coils near theends of the chamber that increase the magnitude of the applied magneticfield at the ends of the chamber. The system may also comprise a beaminjector for injecting a neutralized ion beam into the applied magneticfield, wherein the beam enters an orbit due to the force caused by theapplied magnetic field. In another aspect of the preferred embodiments,the system forms a magnetic field having a topology of a field reversedconfiguration.

In another preferred embodiment, the energy conversion system comprisesinverse cyclotron converters (ICC) coupled to opposing ends of thefusion reactor. The ICC have a hollow cylinder-like geometry formed frommultiple, preferably four or more equal, semi-cylindrical electrodeswith small, straight gaps extending there between. In operation, anoscillating potential is applied to the electrodes in an alternatingfashion. The electric field E within the ICC has a multi-pole structureand vanishes on the symmetry axes and increases linearly with radius;the peak value being at the gap.

In addition, the ICC includes a magnetic field generator for applying auniform uni-directional magnetic field in a direction substantiallyopposite to that of the fusion reactor's containment system. At an endfurthest from the fusion reactor power core the ICC includes an ioncollector. In between the power core and the ICC is a symmetric magneticcusp. wherein the magnetic field of the containment system merges withthe magnetic field of the ICC. An annular shaped electron collector ispositioned about the magnetic cusp and electrically coupled to the ioncollector.

In yet another preferred embodiment, product nuclei andcharge-neutralizing electrons emerge as annular beams from both ends ofthe reactor power core with a density at which the magnetic cuspseparates electrons and ions due to their energy differences. Theelectrons follow magnetic field lines to the electron collector and theions pass through the cusp where the ion trajectories are modified tofollow a substantially helical path along the length of the ICC. Energyis removed from the ions as they spiral past the electrodes, which areconnected to a resonant circuit. The loss of perpendicular energy tendsto be greatest for the highest energy ions that initially circulateclose to the electrodes, where the electric field is strongest.

Other aspects and features of the present invention will become apparentfrom consideration of the following description taken in conjunctionwith the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments are illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings, in whichlike reference numerals refer to like components.

FIG. 1 shows an exemplary confinement chamber of the present invention.

FIG. 2 shows the magnetic field of a FRC.

FIGS. 3A and 3B show, respectively, the diamagnetic and thecounterdiamagnetic direction in a FRC.

FIG. 4 shows the colliding beam system of the present invention.

FIG. 5 shows a betatron orbit.

FIGS. 6A and 6B show, respectively, the magnetic field and the directionof the gradient drift in a FRC.

FIGS. 7A and 7B show, respectively, the electric field and the directionof the {right arrow over (E)}×{right arrow over (B)} drift in a FRC.

FIGS. 8A, 8B and 8C show ion drift orbits.

FIGS. 9A and 9B show the Lorentz force at the ends of a FRC.

FIGS. 10A and 10B show the tuning of the electric field and the electricpotential in the colliding beam system.

FIG. 11 shows a Maxwell distribution.

FIGS. 12A and 12B show transitions from betatron orbits to drift orbitsdue to large-angle, ion-ion collisions.

FIGS. 13 show A, B, C and D betatron orbits when small-angle,electron-ion collisions are considered.

FIG. 14 shows a neutralized ion beam as it is electrically polarizedbefore entering a confining chamber.

FIG. 15 is a head-on view of a neutralized ion beam as it contactsplasma in a confining chamber.

FIG. 16 is a side view schematic of a confining chamber according to apreferred embodiment of a start-up procedure.

FIG. 17 is a side view schematic of a confining chamber according toanother preferred embodiment of a start-up procedure.

FIG. 18 shows traces of B-dot probe indicating the formation of a FRC.

FIG. 19A shows a partial plasma-electric power generation systemcomprising a colliding beam fusion reactor coupled to an inversecyclotron direct energy converter.

FIG. 19B shows an end view of the inverse cyclotron converter in FIG.19A.

FIG. 19C shows an orbit of an ion in the inverse cyclotron converter.

FIG. 20A shows a partial plasma electric power generation systemcomprising a colliding beam fusion reactor coupled to an alternateembodiment of the inverse cyclotron converter.

FIG. 20B shows an end view of the inverse cyclotron converter in FIG.20A.

FIG. 21A shows a particle orbit inside a conventional cyclotron.

FIG. 21B shows an oscillating electric field.

FIG. 21C shows the changing energy of an accelerating particle.

FIG. 22 shows an azimuthal electric field at gaps between the electrodesof the ICC that is experienced by an ion with angular velocity.

FIG. 23 shows a focusing quadrupole doublet lens.

FIGS. 24A and 24B show auxiliary magnetic-field-coil system.

FIG. 25 shows a 100 MW reactor.

FIG. 26 shows reactor support equipment.

FIG. 27 shows a plasma-thrust propulsion system.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

As illustrated in the figures, a plasma-electric power generation systemof the present invention preferably includes a colliding beam fusionreactor coupled to a direct energy conversion system. As alluded toabove, an ideal fusion reactor solves the problem of anomalous transportfor both ions and electrons. The solution to the problem of anomaloustransport found herein makes use of a containment system with a magneticfield having a field reversed configuration (FRC). The anomaloustransport of ions is avoided by magnetic confinement in the FRC in sucha way that the majority of the ions have large, non-adiabatic orbits,making them insensitive to short-wavelength fluctuations that causeanomalous transport of adiabatic ions. In particular, the existence of aregion in the FRC where the magnetic field vanishes makes it possible tohave a plasma comprising a majority of non-adiabatic ions. Forelectrons, the anomalous transport of energy is avoided by tuning theexternally applied magnetic field to develop a strong electric field,which confines them electrostatically in a deep potential well.

Fusion fuel plasmas that can be used with the present confinementapparatus and process are not limited to neutronic fuels such as D-D(Deuterium-Deuterium) or D-T (Deuterium-Tritium), but alsoadvantageously include advanced or aneutronic fuels such as D-He³(Deuterium-helium-3) or p-B¹¹ (hydrogen-Boron-11). (For a discussion ofadvanced fuels, see R. Feldbacher & M. Heindler, Nuclear Instruments andMethods in Physics Research, A271 (1988)JJ-64 (North HollandAmsterdam).) For such aneutronic fuels, the fusion reaction energy isalmost entirely in the form of charged particles, i.e., energetic ions,that can be manipulated in a magnetic field and, depending on the fuel,cause little or no radioactivity. The D-He³ reaction produces an H ionand an He⁴ ion with 18.2 MeV energy while the p-B¹¹ reaction producesthree He⁴ ions and 8.7 MeV energy. Based on theoretical modeling for afusion device utilizing aneutronic fuels, the output energy conversionefficiency may be as high as about 90%, as described by K. Yoshikawa, T.Noma and Y. Yamamoto in Fusion Technology, 19, 870 (1991), for example.Such efficiencies dramatically advance the prospects for aneutronicfusion, in a scalable (1-1000 MW), compact, low-cost configuration.

In a direct energy conversion process of the present invention, thecharged particles of fusion products can be slowed down and theirkinetic energy converted directly to electricity. Advantageously, thedirect energy conversion system of the present invention has theefficiencies, particle-energy tolerances and electronic ability toconvert the frequency and phase of the fusion output power of about 5MHz to match the frequency and phase of an external 60 Hertz power grid.

Fusion Containment System

FIG. 1 illustrates a preferred embodiment of a containment system 300according to the present invention. The containment system 300 comprisesa chamber wall 305 that defines therein a confining chamber 310.Preferably, the chamber 310 is cylindrical in shape, with principle axis315 along the center of the chamber 310. For application of thiscontainment system 300 to a fusion reactor, it is necessary to create avacuum or near vacuum inside the chamber 310. Concentric with theprinciple axis 315 is a betatron flux coil 320, located within thechamber 310. The betatron flux coil 320 comprises an electrical currentcarrying medium adapted to direct current around a long coil, as shown,which preferably comprises parallel windings of multiple separate coilsand, most preferably, parallel windings of about four separate coils, toform a long coil. Persons skilled in the art will appreciate thatcurrent through the betatron coil 320 will result in a magnetic fieldinside the betatron coil 320, substantially in the direction of theprinciple axis 315.

Around the outside of the chamber wall 305 is an outer coil 325. Theouter coil 325 produce a relatively constant magnetic field having fluxsubstantially parallel with principle axis 315. This magnetic field isazimuthally symmetrical. The approximation that the magnetic field dueto the outer coil 325 is constant and parallel to axis 315 is most validaway from the ends of the chamber 310. At each end of the chamber 310 isa mirror coil 330. The mirror coils 330 are adapted to produce anincreased magnetic field inside the chamber 310 at each end, thusbending the magnetic field lines inward at each end. (See FIGS. 8 and10.) As explained, this bending inward of the field lines helps tocontain the plasma 335 in a containment region within the chamber 310generally between the mirror coils 330 by pushing it away from the endswhere it can escape the containment system 300. The mirror coils 330 canbe adapted to produce an increased magnetic field at the ends by avariety of methods known in the art, including increasing the number ofwindings in the mirror coils 330, increasing the current through themirror coils 330, or overlapping the mirror coils 330 with the outercoil 325.

The outer coil 325 and mirror coils 330 are shown in FIG. 1 implementedoutside the chamber wall 305; however, they may be inside the chamber310. In cases where the chamber wall 305 is constructed of a conductivematerial such as metal, it may be advantageous to place the coils 325,330 inside the chamber wall 305 because the time that it takes for themagnetic field to diffuse through the wall 305 may be relatively largeand thus cause the system 300 to react sluggishly. Similarly, thechamber 310 may be of the shape of a hollow cylinder, the chamber wall305 forming a long, annular ring. In such a case, the betatron flux coil320 could be implemented outside of the chamber wall 305 in the centerof that annular ring. Preferably, the inner wall forming the center ofthe annular ring may comprise a non-conducting material such as glass.As will become apparent, the chamber 310 must be of sufficient size andshape to allow the circulating plasma beam or layer 335 to rotate aroundthe principle axis 315 at a given radius.

The chamber wall 305 may be formed of a material having a high magneticpermeability, such as steel. In such a case, the chamber wall 305, dueto induced countercurrents in the material, helps to keep the magneticflux from escaping the chamber 310, “compressing” it. If the chamberwall were to be made of a material having low magnetic permeability,such as plexiglass, another device for containing the magnetic fluxwould be necessary. In such a case, a series of closed-loop, flat metalrings could be provided. These rings, known in the art as fluxdelimiters, would be provided within the outer coils 325 but outside thecirculating plasma beam 335. Further, these flux delimiters could bepassive or active, wherein the active flux delimiters would be drivenwith a predetermined current to greater facilitate the containment ofmagnetic flux within the chamber 310. Alternatively, the outer coils 325themselves could serve as flux delimiters.

As explained in further detail below, a circulating plasma beam 335,comprising charged particles, may be contained within the chamber 310 bythe Lorentz force caused by the magnetic field due to the outer coil325. As such, the ions in the plasma beam 335 are magnetically containedin large betatron orbits about the flux lines from the outer coil 325,which are parallel to the principle axis 315. One or more beam injectionports 340 are also provided for adding plasma ions to the circulatingplasma beam 335 in the chamber 310. In a preferred embodiment, theinjector ports 340 are adapted to inject an ion beam at about the sameradial position from the principle axis 315 where the circulating plasmabeam 335 is contained (i.e., around a null surface described below).Further, the injector ports 340 are adapted to inject ion beams 350 (SeeFIG. 16) tangent to and in the direction of the betatron orbit of thecontained plasma beam 335.

Also provided are one or more background plasma sources 345 forinjecting a cloud of non-energetic plasma into the chamber 310. In apreferred embodiment, the background plasma sources 345 are adapted todirect plasma 335 toward the axial center of the chamber 310. It hasbeen found that directing the plasma this way helps to better containthe plasma 335 and leads to a higher density of plasma 335 in thecontainment region within the chamber 310.

Charged Particles in a FRC

FIG. 2 shows a magnetic field of a FRC 70. The system has cylindricalsymmetry with respect to its axis 78. In the FRC, there are two regionsof magnetic field lines: open 80 and closed 82. The surface dividing thetwo regions is called the separatrix 84. The FRC forms a cylindricalnull surface 86 in which the magnetic field vanishes. In the centralpart 88 of the FRC the magnetic field does not change appreciably in theaxial direction. At the ends 90, the magnetic field does changeappreciably in the axial direction. The magnetic field along the centeraxis 78 reverses direction in the FRC, which gives rise to the term“Reversed” in Field Reversed Configuration (FRC).

In FIG. 3A, the magnetic field outside of the null surface 94 is in afirst direction 96. The magnetic field inside the null surface 94 is ina second direction 98 opposite the first. If an ion moves in thedirection 100, the Lorentz force 30 acting on it points towards the nullsurface 94. This is easily appreciated by applying the right-hand rule.For particles moving in the diamagnetic direction 102, the Lorentz forcealways points toward the null surface 94. This phenomenon gives rise toa particle orbit called betatron orbit, to be described below.

FIG. 3B shows an ion moving in the counterdiamagnetic direction 104. TheLorentz force in this case points away from the null surface 94. Thisphenomenon gives rise to a type of orbit called a drift orbit, to bedescribed below. The diamagnetic direction for ions iscounterdiamagnetic for electrons, and vice versa.

FIG. 4 shows a ring or annular layer of plasma 106 rotating in the ions'diamagnetic direction 102. The ring 106 is located around the nullsurface 86. The magnetic field 108 created by the annular plasma layer106, in combination with an externally applied magnetic field 110, formsa magnetic field having the topology of a FRC (The topology is shown inFIG. 2).

The ion beam that forms the plasma layer 106 has a temperature;therefore, the velocities of the ions form a Maxwell distribution in aframe rotating at the average angular velocity of the ion beam.Collisions between ions of different velocities lead to fusionreactions. For this reason, the plasma beam layer or power core 106 iscalled a colliding beam system.

FIG. 5 shows the main type of ion orbits in a colliding beam system,called a betatron orbit 112. A betatron orbit 112 can be expressed as asine wave centered on the null circle 114. As explained above, themagnetic field on the null circle 114 vanishes. The plane of the orbit112 is perpendicular to the axis 78 of the FRC. Ions in this orbit 112move in their diamagnetic direction 102 from a starting point 116. Anion in a betatron orbit has two motions: an oscillation in the radialdirection (perpendicular to the null circle 114), and a translationalong the null circle 114.

FIG. 6A is a graph of the magnetic field 118 in a FRC. The horizontalaxis of the graph represents the distance in centimeters from the FRCaxis 78. The magnetic field is in kilogauss. As the graph depicts, themagnetic field 118 vanishes at the null circle radius 120.

As shown in FIG. 6B, a particle moving near the null circle will see agradient 126 of the magnetic field pointing away from the null surface86. The magnetic field outside the null circle is in a first direction122, while the magnetic field inside the null circle is in a seconddirection 124 opposite to the first. The direction of a gradient driftis given by the cross product {right arrow over (B)}×∇B, where ∇B is thegradient of the magnetic field; thus, it can be appreciated by applyingthe right-hand rule that the direction of the gradient drift is in thecounterdiamagnetic direction, whether the ion is outside or inside thenull circle 128.

FIG. 7A is a graph of the electric field 130 in a FRC. The horizontalaxis of the graph represents the distance in centimeters from the FRCaxis 78. The electric field is in volts/cm. As the graph depicts, theelectric field 130 vanishes close to the null circle radius 120.

As shown if FIG. 7B, the electric field for ions is deconfining; itpoints in directions 132, 134 away from the null surface 86. Themagnetic field, as before, is in opposite directions 122,124 inside andoutside of the null surface 86. It can be appreciated by applying theright-hand rule that the direction of the {right arrow over (E)}×{rightarrow over (B)} drift is in the diamagnetic direction 102, whether theion is outside or inside the null surface 136.

FIGS. 8A and 8B show another type of common orbit in a FRC, called adrift orbit 138. Drift orbits 138 can be outside of the null surface114, as shown in FIG. 8A, or inside it, as shown in FIG. 8B. Driftorbits 138 rotate in the diamagnetic direction if the {right arrow over(E)}×{right arrow over (B)} drift dominates or in the counterdiamagneticdirection if the gradient drift dominates. The drift orbits 138 shown inFIGS. 8A and 8B rotate in the diamagnetic direction 102 from startingpoint 116.

A drift orbit, as shown in FIG. 8C, can be thought of as a small circlerolling over a relatively bigger circle. The small circle 142 spinsaround its axis in the sense 144. It also rolls over the big circle 146in the direction 102. The point 140 will trace in space a path similarto 138.

FIGS. 9A and 9B show the direction of the Lorentz force at the ends of aFRC 151. In FIG. 9A, an ion is shown moving in the diamagnetic direction102 with a velocity 148 in a magnetic field 150. It can be appreciatedby applying the right-hand rule that the Lorentz force 152 tends to pushthe ion back into the region of closed field lines. In this case,therefore, the Lorentz force 152 is confining for the ions. In FIG. 9B,an ion is shown moving in the counterdiamagnetic direction with avelocity 148 in a magnetic field 150. It can be appreciated by applyingthe right-hand rule that the Lorentz force 152 tends to push the ioninto the region of open field lines. In this case, therefore, theLorentz force 152 is deconfining for the ions.

Magnetic and Electrostatic Confinement in a FRC

A plasma layer 106 (see FIG. 4) can be formed in a FRC by injectingenergetic ion beams around the null surface 86 in the diamagneticdirection 102 of ions. (A detailed discussion of different methods offorming the FRC and plasma ring follows below.) In the circulatingplasma layer 106, most of the ions have betatron orbits 112 (see FIG.5), are energetic, and are non-adiabatic; thus, they are insensitive toshort-wavelength fluctuations that cause anomalous transport.

In a plasma layer 106 formed in a FRC and under equilibrium conditions,the conservation of momentum imposes a relation between the angularvelocity of ions ω_(i) and the angular velocity of electrons ω_(e). Therelation is

$\begin{matrix}{{\omega_{e} = {\omega_{i}\left\lbrack {1 - \frac{\omega_{i}}{\Omega_{0}}} \right\rbrack}},{{{where}\mspace{14mu} \Omega_{0}} = {\frac{{ZeB}_{0}}{m_{i}c}.}}} & (1)\end{matrix}$

In Eq. 1, Z is the ion atomic number, m_(i) is the ion mass, e is theelectron charge, B₀ is the magnitude of the applied magnetic field, andc is the speed of light. There are three free parameters in thisrelation: the applied magnetic field B₀, the electron angular velocityω_(e), and the ion angular velocity ω_(i). If two of them are known, thethird can be determined from Eq. 1.

Because the plasma layer 106 is formed by injecting ion beams into theFRC, the angular velocity of ions ω_(i) is determined by the injectionkinetic energy of the beam W_(i), which is given by

$\begin{matrix}{W_{i} = {{\frac{1}{2}m_{i}V_{i}^{2}} = {\frac{1}{2}{m_{i}\left( {\omega_{i}r_{o}} \right)}^{2}}}} & (2)\end{matrix}$

Here, V_(i)=ω_(i)r₀, where V_(i) is the injection velocity of ions,ω_(i) is the cyclotron frequency of ions, and r₀ is the radius of thenull surface 86. The kinetic energy of electrons in the beam has beenignored because the electron mass m_(e) is much smaller than the ionmass m_(i).

For a fixed injection velocity of the beam (fixed ω_(i)), the appliedmagnetic field B₀ can be tuned so that different values of ω_(e) areobtainable. As will be shown, tuning the external magnetic field B₀ alsogives rise to different values of the electrostatic field inside theplasma layer. This feature of the invention is illustrated in FIGS. 10Aand 10B. FIG. 10A shows three plots of the electric field (in volts/cm)obtained for the same injection velocity, ω_(i)=1.35×10⁷ s⁻¹, but forthree different values of the applied magnetic field B₀:

Plot Applied magnetic field (B₀) electron angular velocity (ω_(e)) 154B₀ = 2.77 kG ω_(e) = 0 156 B₀ = 5.15 kG ω_(e) = 0.625 × 10⁷ s⁻¹ 158 B₀ =15.5 kG ω_(e) = 1.11 × 10⁷ s⁻¹The values of ω_(e) in the table above were determined according toEq. 1. One can appreciate that ω_(e)>0 means that Ω₀>ω_(i) in Eq. 1, sothat electrons rotate in their counterdiamagnetic direction. FIG. 10Bshows the electric potential (in volts) for the same set of values of B₀and ω_(e). The horizontal axis, in FIGS. 10A and 10B, represents thedistance from the FRC axis 78, shown in the graph in centimeters. Theelectric field and electric potential depend strongly on ω_(e).

The above results can be explained on simple physical grounds. When theions rotate in the diamagnetic direction, the ions are confinedmagnetically by the Lorentz force. This was shown in FIG. 3A. Forelectrons, rotating in the same direction as the ions, the Lorentz forceis in the opposite direction, so that electrons would not be confined.The electrons leave the plasma and, as a result, a surplus of positivecharge is created. This sets up an electric field that prevents otherelectrons from leaving the plasma. The direction and the magnitude ofthis electric field, in equilibrium, is determined by the conservationof momentum.

The electrostatic field plays an essential role on the transport of bothelectrons and ions. Accordingly, an important aspect of this inventionis that a strong electrostatic field is created inside the plasma layer106, the magnitude of this electrostatic field is controlled by thevalue of the applied magnetic field B₀ which can be easily adjusted.

As explained, the electrostatic field is confining for electrons ifω_(e)>0. As shown in FIG. 10B, the depth of the well can be increased bytuning the applied magnetic field B₀. Except for a very narrow regionnear the null circle, the electrons always have a small gyroradius.Therefore, electrons respond to short-wavelength fluctuations with ananomalously fast diffusion rate. This diffusion, in fact, helps maintainthe potential well once the fusion reaction occurs. The fusion productions, being of much higher energy, leave the plasma. To maintain chargequasi-neutrality, the fusion products must pull electrons out of theplasma with them, mainly taking the electrons from the surface of theplasma layer. The density of electrons at the surface of the plasma isvery low, and the electrons that leave the plasma with the fusionproducts must be replaced; otherwise, the potential well woulddisappear.

FIG. 11 shows a Maxwellian distribution 162 of electrons. Only veryenergetic electrons from the tail 160 of the Maxwell distribution canreach the surface of the plasma and leave with fusion ions. The tail 160of the distribution 162 is thus continuously created byelectron-electron collisions in the region of high density near the nullsurface. The energetic electrons still have a small gyroradius, so thatanomalous diffusion permits them to reach the surface fast enough toaccommodate the departing fusion product ions. The energetic electronslose their energy ascending the potential well and leave with verylittle energy. Although the electrons can cross the magnetic fieldrapidly, due to anomalous transport, anomalous energy losses tend to beavoided because little energy is transported.

Another consequence of the potential well is a strong cooling mechanismfor electrons that is similar to evaporative cooling. For example, forwater to evaporate, it must be supplied the latent heat of vaporization.This heat is supplied by the remaining liquid water and the surroundingmedium, which then thermalize rapidly to a lower temperature faster thanthe heat transport processes can replace the energy. Similarly, forelectrons, the potential well depth is equivalent to water's latent heatof vaporization. The electrons supply the energy required to ascend thepotential well by the thermalization process that re-supplies the energyof the Maxwell tail so that the electrons can escape. The thermalizationprocess thus results in a lower electron temperature, as it is muchfaster than any heating process. Because of the mass difference betweenelectrons and protons, the energy transfer time from protons is about1800 times less than the electron thermalization time. This coolingmechanism also reduces the radiation loss of electrons. This isparticularly important for advanced fuels, where radiation losses areenhanced by fuel ions with an atomic number Z greater than 1; Z>1.

The electrostatic field also affects ion transport. The majority ofparticle orbits in the plasma layer 106 are betatron orbits 112.Large-angle collisions, that is, collisions with scattering anglesbetween 90° and 180°, can change a betatron orbit to a drift orbit. Asdescribed above, the direction of rotation of the drift orbit isdetermined by a competition between the {right arrow over (E)}×{rightarrow over (B)} drift and the gradient drift. If the {right arrow over(E)}×{right arrow over (B)} drift dominates, the drift orbit rotates inthe diamagnetic direction. If the gradient drift dominates, the driftorbit rotates in the counterdiamagnetic direction. This is shown inFIGS. 12A and 12B. FIG. 12A shows a transition from a betatron orbit toa drift orbit due to a 180° collision, which occurs at the point 172.The drift orbit continues to rotate in the diamagnetic direction becausethe {right arrow over (E)}×{right arrow over (B)} drift dominates. FIG.12B shows another 180° collision, but in this case the electrostaticfield is weak and the gradient drift dominates. The drift orbit thusrotates in the counterdiamagnetic direction.

The direction of rotation of the drift orbit determines whether it isconfined or not. A particle moving in a drift orbit will also have avelocity parallel to the FRC axis. The time it takes the particle to gofrom one end of the FRC to the other, as a result of its parallelmotion, is called transit time; thus, the drift orbits reach an end ofthe FRC in a time of the order of the transit time. As shown inconnection with FIG. 9A, the Lorentz force at the ends of the FRC isconfining only for drift orbits rotating in the diamagnetic direction.After a transit time, therefore, ions in drift orbits rotating in thecounterdiamagnetic direction are lost.

This phenomenon accounts for a loss mechanism for ions, which isexpected to have existed in all FRC experiments. In fact, in theseexperiments, the ions carried half of the current and the electronscarried the other half. In these conditions the electric field insidethe plasma was negligible, and the gradient drift always dominated the{right arrow over (E)}×{right arrow over (B)} drift. Hence, all thedrift orbits produced by large-angle collisions were lost after atransit time. These experiments reported ion diffusion rates that werefaster than those predicted by classical diffusion estimates.

If there is a strong electrostatic field, the {right arrow over(E)}×{right arrow over (B)} drift dominates the gradient drift, and thedrift orbits rotate in the diamagnetic direction. This was shown abovein connection with FIG. 12A. When these orbits reach the ends of theFRC, they are reflected back into the region of closed field lines bythe Lorentz force; thus, they remain confined in the system.

The electrostatic fields in the colliding beam system may be strongenough, so that the {right arrow over (E)}×{right arrow over (B)} driftdominates the gradient drift. Thus, the electrostatic field of thesystem would avoid ion transport by eliminating this ion loss mechanism,which is similar to a loss cone in a mirror device.

Another aspect of ion diffusion can be appreciated by considering theeffect of small-angle, electron-ion collisions on betatron orbits. FIG.13A shows a betatron orbit 112; FIG. 13B shows the same orbit 112 whensmall-angle electron-ion collisions are considered 174; FIG. 13C showsthe orbit of FIG. 13B followed for a time that is longer by a factor often 176; and FIG. 13D shows the orbit of FIG. 13B followed for a timelonger by a factor of twenty 178. It can be seen that the topology ofbetatron orbits does not change due to small-angle, electron-ioncollisions; however, the amplitude of their radial oscillations growswith time. In fact, the orbits shown in FIGS. 13A to 13D fatten out withtime, which indicates classical diffusion.

Formation of the FRC

Conventional procedures used to form a FRC primarily employ the thetapinch-field reversal procedure. In this conventional method, a biasmagnetic field is applied by external coils surrounding a neutral gasback-filled chamber. Once this has occurred, the gas is ionized and thebias magnetic field is frozen in the plasma. Next, the current in theexternal coils is rapidly reversed and the oppositely oriented magneticfield lines connect with the previously frozen lines to form the closedtopology of the FRC (see FIG. 2). This formation process is largelyempirical and there exists almost no means of controlling the formationof the FRC. The method has poor reproducibility and no tuning capabilityas a result.

In contrast, the FRC formation methods of the present invention allowfor ample control and provide a much more transparent and reproducibleprocess. In fact, the FRC formed by the methods of the present inventioncan be tuned and its shape as well as other properties can be directlyinfluenced by manipulation of the magnetic field applied by the outerfield coils 325. Formation of the FRC by methods of the presentinventions also results in the formation of the electric field andpotential well in the manner described in detail above. Moreover, thepresent methods can be easily extended to accelerate the FRC to reactorlevel parameters and high-energy fuel currents, and advantageouslyenables the classical confinement of the ions. Furthermore, thetechnique can be employed in a compact device and is very robust as wellas easy to implement—all highly desirable characteristics for reactorsystems.

In the present methods, FRC formation relates to the circulating plasmabeam 335. It can be appreciated that the circulating plasma beam 335,because it is a current, creates a poloidal magnetic field, as would anelectrical current in a circular wire. Inside the circulating plasmabeam 335, the magnetic self-field that it induces opposes the externallyapplied magnetic field due to the outer coil 325. Outside the plasmabeam 335, the magnetic self-field is in the same direction as theapplied magnetic field. When the plasma ion current is sufficientlylarge, the self-field overcomes the applied field, and the magneticfield reverses inside the circulating plasma beam 335, thereby formingthe FRC topology as shown in FIGS. 2 and 4.

The requirements for field reversal can be estimated with a simplemodel. Consider an electric current I_(P) carried by a ring of majorradius r₀ and minor radius a<<r₀. The magnetic field at the center ofthe ring normal to the ring is B_(p)=2πI_(P)/(cr_(o)). Assume that thering current I_(P)=N_(p)e(Ω₀/2π) is carried by N_(p) ions that have anangular velocity Ω₀. For a single ion circulating at radius r₀=V₀/Ω₀,Ω₀=eB₀/m_(i)c is the cyclotron frequency for an external magnetic fieldB₀. Assume V₀ is the average velocity of the beam ions. Field reversalis defined as

$\begin{matrix}{{B_{p} = {\frac{N_{p}e\; \Omega_{0}}{r_{0}c} \geq {2B_{0}}}},} & (3)\end{matrix}$

which implies that N_(p)>2 r₀/α_(i), and

$\begin{matrix}{{I_{p} \geq \frac{{eV}_{0}}{\pi \; \alpha_{i}}},} & (4)\end{matrix}$

where α_(i)=e²/m_(i)c²=1.57×10⁻¹⁶ cm and the ion beam energy is

$\frac{1}{2}m_{i}{V_{0}^{2}.}$

In the one-dimensional model, the magnetic field from the plasma currentis B_(p)=(2π/c)i_(p), where i_(p) is current per unit of length. Thefield reversal requirement is i_(p)>eV₀/πr₀α_(i)=0.225 kA/cm, whereB₀=69.3 G and

${\frac{1}{2}m_{i}V_{0}^{2}} = {100\mspace{11mu} {{eV}.}}$

For a model with periodic rings and B_(z) is averaged over the axialcoordinate

B_(z)

=(2π/c)(I_(p)/s) (s is the ring spacing), if s=r₀, this model would havethe same average magnetic field as the one dimensional model withi_(p)=I_(p)/s.

Combined Beam/Betatron Formation Technique

A preferred method of forming a FRC within the confinement system 300described above is herein termed the combined beam/betatron technique.This approach combines low energy beams of plasma ions with betatronacceleration using the betatron flux coil 320.

The first step in this method is to inject a substantially annular cloudlayer of background plasma in the chamber 310 using the backgroundplasma sources 345. Outer coil 325 produces a magnetic field inside thechamber 310, which magnetizes the background plasma. At short intervals,low energy ion beams are injected into the chamber 310 through theinjector ports 340 substantially transverse to the externally appliedmagnetic field within the chamber 310. As explained above, the ion beamsare trapped within the chamber 310 in large betatron orbits by thismagnetic field. The ion beams may be generated by an ion accelerator,such as an accelerator comprising an ion diode and a Marx generator.(see R. B. Miller, An Introduction to the Physics of Intense ChargedParticle Beams, (1982)). As one of skill in the art can appreciate, theexternally applied magnetic field will exert a Lorentz force on theinjected ion beam as soon as it enters the chamber 310; however, it isdesired that the beam not deflect, and thus not enter a betatron orbit,until the ion beam reaches the circulating plasma beam 335. To solvethis problem, the ion beams are neutralized with electrons and directedthrough a substantially constant unidirectional magnetic field beforeentering the chamber 310. As illustrated in FIG. 14, when the ion beam350 is directed through an appropriate magnetic field, the positivelycharged ions and negatively charged electrons separate. The ion beam 350thus acquires an electric self-polarization due to the magnetic field.This magnetic field may be produced by, e.g., a permanent magnet or byan electromagnet along the path of the ion beam. When subsequentlyintroduced into the confinement chamber 310, the resultant electricfield balances the magnetic force on the beam particles, allowing theion beam to drift undeflected. FIG. 15 shows a head-on view of the ionbeam 350 as it contacts the plasma 335. As depicted, electrons from theplasma 335 travel along magnetic field lines into or out of the beam350, which thereby drains the beam's electric polarization. When thebeam is no longer electrically polarized, the beam joins the circulatingplasma beam 335 in a betatron orbit around the principle axis 315, asshown in FIG. 1 (see also FIG. 4).

When the plasma beam 335 travels in its betatron orbit, the moving ionscomprise a current, which in turn gives rise to a poloidal magneticself-field. To produce the FRC topology within the chamber 310, it isnecessary to increase the velocity of the plasma beam 335, thusincreasing the magnitude of the magnetic self-field that the plasma beam335 causes. When the magnetic self-field is large enough, the directionof the magnetic field at radial distances from the axis 315 within theplasma beam 335 reverses, giving rise to a FRC. (See FIGS. 2 and 4). Itcan be appreciated that, to maintain the radial distance of thecirculating plasma beam 335 in the betatron orbit, it is necessary toincrease the applied magnetic field from the outer coil 325 as theplasma beam 335 increases in velocity. A control system is thus providedfor maintaining an appropriate applied magnetic field, dictated by thecurrent through the outer coil 325. Alternatively, a second outer coilmay be used to provide the additional applied magnetic field that isrequired to maintain the radius of the plasma beam's orbit as it isaccelerated.

To increase the velocity of the circulating plasma beam 335 in itsorbit, the betatron flux coil 320 is provided. Referring to FIG. 16, itcan be appreciated that increasing a current through the betatron fluxcoil 320, by Ampere's Law, induces an azimuthal electric field, E,inside the chamber 310. The positively charged ions in the plasma beam335 are accelerated by this induced electric field, leading to fieldreversal as described above. When ion beams are added to the circulatingplasma beam 335, as described above, the plasma beam 335 depolarizes theion beams.

For field reversal, the circulating plasma beam 335 is preferablyaccelerated to a rotational energy of about 100 eV, and preferably in arange of about 75 eV to 125 eV. To reach fusion relevant conditions, thecirculating plasma beam 335 is preferably accelerated to about 200 keVand preferably to a range of about 100 keV to 3.3 MeV.

FRC formation was successfully demonstrated utilizing the combinedbeam/betatron formation technique. The combined beam/betatron formationtechnique was performed experimentally in a chamber 1 m in diameter and1.5 m in length using an externally applied magnetic field of up to 500G, a magnetic field from the betatron flux coil 320 of up to 5 kG, and avacuum of 1.2×10⁻⁵ torr. In the experiment, the background plasma had adensity of 10¹³ cm⁻³ and the ion beam was a neutralized Hydrogen beamhaving a density of 1.2×10¹³ cm⁻³, a velocity of 2×10⁷ cm/s, and a pulselength of around 20 μs (at half height). Field reversal was observed.

Betatron Formation Technique

Another preferred method of forming a FRC within the confinement system300 is herein termed the betatron formation technique. This technique isbased on driving the betatron induced current directly to accelerate acirculating plasma beam 335 using the betatron flux coil 320. Apreferred embodiment of this technique uses the confinement system 300depicted in FIG. 1, except that the injection of low energy ion beams isnot necessary.

As indicated, the main component in the betatron formation technique isthe betatron flux coil 320 mounted in the center and along the axis ofthe chamber 310. Due to its separate parallel windings construction, thecoil 320 exhibits very low inductance and, when coupled to an adequatepower source, has a low LC time constant, which enables rapid ramp up ofthe current in the flux coil 320.

Preferably, formation of the FRC commences by energizing the externalfield coils 325, 330. This provides an axial guide field as well asradial magnetic field components near the ends to axially confine theplasma injected into the chamber 310. Once sufficient magnetic field isestablished, the background plasma sources 345 are energized from theirown power supplies. Plasma emanating from the guns streams along theaxial guide field and spreads slightly due to its temperature. As theplasma reaches the mid-plane of the chamber 310, a continuous, axiallyextending, annular layer of cold, slowly moving plasma is established.

At this point the betatron flux coil 320 is energized. The rapidlyrising current in the coil 320 causes a fast changing axial flux in thecoil's interior. By virtue of inductive effects this rapid increase inaxial flux causes the generation of an azimuthal electric field E (seeFIG. 17), which permeates the space around the flux coil. By Maxwell'sequations, this electric field E is directly proportional to the changein strength of the magnetic flux inside the coil, i.e.: a fasterbetatron coil current ramp-up will lead to a stronger electric field.

The inductively created electric field E couples to the chargedparticles in the plasma and causes a ponderomotive force, whichaccelerates the particles in the annular plasma layer. Electrons, byvirtue of their smaller mass, are the first species to experienceacceleration. The initial current formed by this process is, thus,primarily due to electrons. However, sufficient acceleration time(around hundreds of micro-seconds) will eventually also lead to ioncurrent. Referring to FIG. 17, this electric field E accelerates theelectrons and ions in opposite directions. Once both species reach theirterminal velocities, current is carried about equally by ions andelectrons.

As noted above, the current carried by the rotating plasma gives rise toa self magnetic field. The creation of the actual FRC topology sets inwhen the self magnetic field created by the current in the plasma layerbecomes comparable to the applied magnetic field from the external fieldcoils 325, 330. At this point magnetic reconnection occurs and the openfield lines of the initial externally produced magnetic field begin toclose and form the FRC flux surfaces (see FIGS. 2 and 4).

The base FRC established by this method exhibits modest magnetic fieldand particle energies that are typically not at reactor relevantoperating parameters. However, the inductive electric acceleration fieldwill persist, as long as the current in the betatron flux coil 320continues to increase at a rapid rate. The effect of this process isthat the energy and total magnetic field strength of the FRC continuesto grow. The extent of this process is, thus, primarily limited by theflux coil power supply, as continued delivery of current requires amassive energy storage bank. However, it is, in principal,straightforward to accelerate the system to reactor relevant conditions.

For field reversal, the circulating plasma beam 335 is preferablyaccelerated to a rotational energy of about 100 eV, and preferably in arange of about 75 eV to 125 eV. To reach fusion relevant conditions, thecirculating plasma beam 335 is preferably accelerated to about 200 keVand preferably to a range of about 100 keV to 3.3 MeV. When ion beamsare added to the circulating plasma beam 335, as described above, theplasma beam 335 depolarizes the ion beams.

FRC formation utilizing the betatron formation technique wassuccessfully demonstrated at the following parameter levels:

-   -   Vacuum chamber dimensions: about 1 m diameter, 1.5 m length.    -   Betatron coil radius of 10 cm.    -   Plasma orbit radius of 20 cm.    -   Mean external magnetic field produced in the vacuum chamber was        up to 100 Gauss, with a ramp-up period of 150 μs and a mirror        ratio of 2 to 1. (Source: Outer coils and betatron coils).    -   The background plasma (substantially Hydrogen gas) was        characterized by a mean density of about 10¹³ cm⁻³, kinetic        temperature of less than 10 eV.    -   The lifetime of the configuration was limited by the total        energy stored in the experiment and generally was around 30 μs.

The experiments proceeded by first injecting a background plasma layerby two sets of coaxial cable guns mounted in a circular fashion insidethe chamber. Each collection of 8 guns was mounted on one of the twomirror coil assemblies. The guns were azimuthally spaced in anequidistant fashion and offset relative to the other set. Thisarrangement allowed for the guns to be fired simultaneously and therebycreated an annular plasma layer.

Upon establishment of this layer, the betatron flux coil was energized.Rising current in the betatron coil windings caused an increase in fluxinside the coil, which gave rise to an azimuthal electric field curlingaround the betatron coil. Quick ramp-up and high current in the betatronflux coil produced a strong electric field, which accelerated theannular plasma layer and thereby induced a sizeable current.Sufficiently strong plasma current produced a magnetic self-field thataltered the externally supplied field and caused the creation of thefield reversed configuration. Detailed measurements with B-dot loopsidentified the extent, strength and duration of the FRC.

An example of typical data is shown by the traces of B-dot probe signalsin FIG. 18. The data curve A represents the absolute strength of theaxial component of the magnetic field at the axial mid-plane (75 cm fromeither end plate) of the experimental chamber and at a radial positionof 15 cm. The data curve B represents the absolute strength of the axialcomponent of the magnetic field at the chamber axial mid-plane and at aradial position of 30 cm. The curve A data set, therefore, indicatesmagnetic field strength inside of the fuel plasma layer (betweenbetatron coil and plasma) while the curve B data set depicts themagnetic field strength outside of the fuel plasma layer. The dataclearly indicates that the inner magnetic field reverses orientation (isnegative) between about 23 and 47 μs, while the outer field stayspositive, i.e., does not reverse orientation. The time of reversal islimited by the ramp-up of current in the betatron coil. Once peakcurrent is reached in the betatron coil, the induced current in the fuelplasma layer starts to decrease and the FRC rapidly decays. Up to nowthe lifetime of the FRC is limited by the energy that can be stored inthe experiment. As with the injection and trapping experiments, thesystem can be upgraded to provide longer FRC lifetime and accelerationto reactor relevant parameters.

Overall, this technique not only produces a compact FRC, but it is alsorobust and straightforward to implement. Most importantly, the base FRCcreated by this method can be easily accelerated to any desired level ofrotational energy and magnetic field strength. This is crucial forfusion applications and classical confinement of high-energy fuel beams.

Fusion

Significantly, these two techniques for forming a FRC inside of acontainment system 300 described above, or the like, can result inplasmas having properties suitable for causing nuclear fusion therein.More particularly, the FRC formed by these methods can be accelerated toany desired level of rotational energy and magnetic field strength. Thisis crucial for fusion applications and classical confinement ofhigh-energy fuel beams. In the confinement system 300, therefore, itbecomes possible to trap and confine high-energy plasma beams forsufficient periods of time to cause a fusion reaction therewith.

To accommodate fusion, the FRC formed by these methods is preferablyaccelerated to appropriate levels of rotational energy and magneticfield strength by betatron acceleration. Fusion, however, tends torequire a particular set of physical conditions for any reaction to takeplace. In addition, to achieve efficient burn-up of the fuel and obtaina positive energy balance, the fuel has to be kept in this statesubstantially unchanged for prolonged periods of time. This isimportant, as high kinetic temperature and/or energy characterize afusion relevant state. Creation of this state, therefore, requiressizeable input of energy, which can only be recovered if most of thefuel undergoes fusion. As a consequence, the confinement time of thefuel has to be longer than its burn time. This leads to a positiveenergy balance and consequently net energy output.

A significant advantage of the present invention is that the confinementsystem and plasma described herein are capable of long confinementtimes, i.e., confinement times that exceed fuel burn times. A typicalstate for fusion is, thus, characterized by the following physicalconditions (which tend to vary based on fuel and operating mode):

Average ion temperature: in a range of about 30 to 230 keV andpreferably in a range of about 80 keV to 230 keV.

Average electron temperature: in a range of about 30 to 100 keV andpreferably in a range of about 80 to 100 keV.

Coherent energy of the fuel beams (injected ion beams and circulatingplasma beam): in a range of about 100 keV to 3.3 MeV and preferably in arange of about 300 keV to 3.3 MeV.

Total magnetic field: in a range of about 47.5 to 120 kG and preferablyin a range of about 95 to 120 kG (with the externally applied field in arange of about 2.5 to 15 kG and preferably in a range of about 5 to 15kG).

Classical Confinement time: greater than the fuel burn time andpreferably in a range of about 10 to 100 seconds.

Fuel ion density: in a range of about 10¹⁴ to less than 10¹⁶ cm⁻³ andpreferably in a range of about 10¹⁴ to 10¹⁵ cm⁻³.

Total Fusion Power: preferably in a range of about 50 to 450 kW/cm(power per cm of chamber length)

To accommodate the fusion state illustrated above, the FRC is preferablyaccelerated to a level of coherent rotational energy preferably in arange of about 100 keV to 3.3 MeV, and more preferably in a range ofabout 300 keV to 3.3 MeV, and a level of magnetic field strengthpreferably in a range of about 45 to 120 kG, and more preferably in arange of about 90 to 115 kG. At these levels, high energy ion beams canbe injected into the FRC and trapped to form a plasma beam layer whereinthe plasma beam ions are magnetically confined and the plasma beamelectrons are electrostatically confined.

Preferably, the electron temperature is kept as low as practicallypossible to reduce the amount of bremsstrahlung radiation, which can,otherwise, lead to radiative energy losses. The electrostatic energywell of the present invention provides an effective means ofaccomplishing this.

The ion temperature is preferably kept at a level that provides forefficient bum-up since the fusion cross-section is a function of iontemperature. High direct energy of the fuel ion beams is essential toprovide classical transport as discussed in this application. It alsominimizes the effects of instabilities on the fuel plasma. The magneticfield is consistent with the beam rotation energy. It is partiallycreated by the plasma beam (self-field) and in turn provides the supportand force to keep the plasma beam on the desired orbit.

Fusion Products

The fusion products are born in the power core predominantly near thenull surface 86 from where they emerge by diffusion towards theseparatrix 84 (see FIGS. 2 and 4). This is due to collisions withelectrons (as collisions with ions do not change the center of mass andtherefore do not cause them to change field lines). Because of theirhigh kinetic energy (product ions have much higher energy than the fuelions), the fusion products can readily cross the separatrix 84. Oncethey are beyond the separatrix 84, they can leave along the open fieldlines 80 provided that they experience scattering from ion-ioncollisions. Although this collisional process does not lead todiffusion, it can change the direction of the ion velocity vector suchthat it points parallel to the magnetic field. These open field lines 80connect the FRC topology of the core with the uniform applied fieldprovided outside the FRC topology. Product ions emerge on differentfield lines, which they follow with a distribution of energies.Advantageously, the product ions and charge-neutralizing electronsemerge in the form of rotating annular beams from both ends of the fuelplasma. For example for a 50 MW design of a p-B¹¹ reaction, these beamswill have a radius of about 50 centimeters and a thickness of about 10centimeters. In the strong magnetic fields found outside the separatrix84 (typically around 100 kG), the product ions have an associateddistribution of gyro-radii that varies from a minimum value of about 1cm to a maximum of around 3 cm for the most energetic product ions.

Initially the product ions have longitudinal as well as rotationalenergy characterized by ½ M(v_(par))² and ½ M(V_(perp))². v_(perp) isthe azimuthal velocity associated with rotation around a field line asthe orbital center. Since the field lines spread out after leaving thevicinity of the FRC topology, the rotational energy tends to decreasewhile the total energy remains constant. This is a consequence of theadiabatic invariance of the magnetic moment of the product ions. It iswell known in the art that charged particles orbiting in a magneticfield have a magnetic moment associated with their motion. In the caseof particles moving along a slow changing magnetic field, there alsoexists an adiabatic invariant of the motion described by ½M(v_(perp))²/B. The product ions orbiting around their respective fieldlines have a magnetic moment and such an adiabatic invariant associatedwith their motion. Since B decreases by a factor of about 10 (indicatedby the spreading of the field lines), it follows that v_(perp) willlikewise decrease by about 3.2. Thus, by the time the product ionsarrive at the uniform field region their rotational energy would be lessthan 5% of their total energy; in other words almost all the energy isin the longitudinal component.

Energy Conversion

The direct energy conversion system of the present invention comprisesan inverse cyclotron converter (ICC) 420 shown in FIGS. 19A and 20Acoupled to a (partially illustrated) power core 436 of a colliding beamfusion reactor (CBFR) 410 to form a plasma-electric power generationsystem 400. A second ICC (not shown) may be disposed symmetrically tothe left of the CBFR 410. A magnetic cusp 486 is located between theCBFR 410 and the ICC 420 and is formed when the CBFR 410 and ICC 420magnetic fields merge.

Before describing the ICC 420 and its operation in detail, a review of atypical cyclotron accelerator is provided. In conventional cyclotronaccelerators, energetic ions with velocities perpendicular to a magneticfield rotate in circles. The orbit radius of the energetic ions isdetermined by the magnetic field strength and their charge-to-massratio, and increases with energy. However, the rotation frequency of theions is independent of their energy. This fact has been exploited in thedesign of cyclotron accelerators.

Referring to FIG. 21A, a conventional cyclotron accelerator 700 includestwo mirror image C-shaped electrodes 710 forming mirror image D-shapedcavities placed in a homogenous magnetic field 720 having field linesperpendicular to the electrodes' plane of symmetry, i.e., the plane ofthe page. An oscillating electric potential is applied between theC-shaped electrodes (see FIG. 21B). Ions I are emitted from a sourceplaced in the center of the cyclotron 700. The magnetic field 720 isadjusted so that the rotation frequency of the ions matches that of theelectric potential and associated electric field. If an ion I crossesthe gap 730 between the C-shaped electrodes 710 in the same direction asthat of the electric field, it is accelerated. By accelerating the ionI, its energy and orbit radius increase. When the ion has traveled ahalf-circle arc (experiencing no increase in energy), it crosses the gap730 again. Now the electric field between the C-shaped electrodes 710has reversed direction. The ion I is again accelerated, and its energyis further increased. This process is repeated every time the ioncrosses the gap 730 provided its rotation frequency continues to matchthat of the oscillating electric field (see FIG. 21C). If on the otherhand a particle crosses the gap 730 when the electric field is in theopposite direction it will be decelerated and returned to the source atthe center. Only particles with initial velocities perpendicular to themagnetic field 720 and that cross the gaps 730 in the proper phase ofthe oscillating electric field will be accelerated. Thus, proper phasematching is essential for acceleration.

In principle, a cyclotron could be used to extract kinetic energy from apencil beam of identical energetic ions. Deceleration of ions with acyclotron, but without energy extraction has been observed for protons,as described by Bloch and Jeffries in Phys. Rev. 80, 305 (1950). Theions could be injected into the cavity such that they are brought into adecelerating phase relative to the oscillating field. All of the ionswould then reverse the trajectory T of the accelerating ion shown inFIG. 21A. As the ions slow down due to interaction with the electricfield, their kinetic energy is transformed into oscillating electricenergy in the electric circuit of which the cyclotron is part. Directconversion to electric energy would be achieved, tending to occur withvery high efficiency.

In practice, the ions of an ion beam would enter the cyclotron with allpossible phases. Unless the varying phases are compensated for in thedesign of the cyclotron, half of the of the ions would be acceleratedand the other half decelerated. As a result, the maximum conversionefficiency would effectively be 50%. Moreover the annular fusion production beams discussed above are of an unsuitable geometry for theconventional cyclotron.

As discussed in greater detail below, the ICC of the present inventionaccommodates the annular character of the fusion product beams exitingthe FRC of fusion reactor power core, and the random relative phase ofthe ions within the beam and the spread of their energies.

Referring back to FIG. 19A, a portion of a power core 436 of the CBFR410 is illustrated on the left side, wherein a plasma fuel core 435 isconfined in a FRC 470 formed in part due to a magnetic field applied byoutside field coils 425. The FRC 470 includes closed field lines 482, aseparatrix 484 and open field lines 480, which, as noted above,determines the properties of the annular beam 437 of the fusionproducts. The open field lines 480 extend away from the power core 436towards the magnetic cusp 486. As noted above, fusion products emergefrom the power core 436 along open field lines 480 in the form of anannular beam 437 comprising energetic ions and charge neutralizingelectrons.

The geometry of the ICC 420 is like a hollow cylinder with a length ofabout five meters. Preferably, four or more equal, semi-cylindricalelectrodes 494 with small, straight gaps 497 make up the cylindersurface. In operation, an oscillating potential is applied to theelectrodes 494 in an alternating fashion. The electric field E withinthe converter has a quadrupole structure as indicated in the end viewillustrated in FIG. 19B. The electric field E vanishes on the symmetryaxis and increases linearly with the radius; the peak value is at thegap 497.

In addition, the ICC 420 includes outside field coils 488 to form auniform field within the ICC's hollow cylinder geometry. Because thecurrent runs through the ICC field coils 488 in a direction opposite tothe direction of the current running through the CBFR field coils 425,the field lines 496 in the ICC 420 run in a direction opposite to thedirection of the open field lines 480 of the CBFR 410. At an endfurthest from the power core 436 of the CBFR 410, the ICC 420 includesan ion collector 492.

In between the CBFR 410 and the ICC 420 is a symmetric magnetic cusp 486wherein the open field lines 480 of the CBFR 410 merge with the fieldlines 496 of the ICC 420. An annular shaped electron collector 490 isposition about the magnetic cusp 486 and electrically coupled to the ioncollector 498. As discussed below, the magnetic field of the magneticcusps 486 converts the axial velocity of the beam 437 to a rotationalvelocity with high efficiency. FIG. 19C illustrates a typical ion orbit422 within the converter 420.

The CBFR 410 has a cylindrical symmetry. At its center is the fusionpower core 436 with a fusion plasma core 435 contained in a FRC 470magnetic field topology in which the fusion reactions take place. Asnoted, the product nuclei and charge-neutralizing electrons emerge asannular beams 437 from both ends of the fuel plasma 435. For example fora 50 MW design of a p-B¹¹ reaction, these beams will have a radius ofabout 50 cm and a thickness of about 10 cm. The annular beam has adensity n≅10⁷-10⁸ cm³. For such a density, the magnetic cusp 486separates the electrons and ions. The electrons follow the magneticfield lines to the electron collector 490 and the ions pass through thecusp 486 where the ion trajectories are modified to follow asubstantially helical path along the length of the ICC 420. Energy isremoved from the ions as they spiral past the electrodes 494 connectedto a resonant circuit (not shown). The loss of perpendicular energy isgreatest for the highest energy ions that initially circulate close tothe electrodes 494, where the electric field is strongest.

The ions arrive at the magnetic cusp 486 with the rotational energyapproximately equal to the initial total energy, i.e., ½ Mv_(P) ²≅½ Mv₀². There is a distribution of ion energies and ion initial radii r₀ whenthe ions reach the magnetic cusp 486. However, the initial radii r₀tends to be approximately proportional to the initial velocity v₀. Theradial magnetic field and the radial beam velocity produce a Lorentzforce in the azimuthal direction. The magnetic field at the cusp 486does not change the particle energy but converts the initial axialvelocity v_(P)≅v₀ to a residual axial velocity v_(z) and an azimuthalvelocity v_(⊥), where v₀ ²=v_(z) ²+v_(⊥) ². The value of the azimuthalvelocity v_(⊥) can be determined from the conservation of canonicalmomentum

$\begin{matrix}{P_{\theta} = {{{{Mr}_{0}v_{\bot}} - \frac{{qB}_{0}r_{0}^{2}}{2c}} = \frac{{qB}_{0}r_{0}^{2}}{2c}}} & (5)\end{matrix}$

A beam ion enters the left hand side of the cusp 486 with B_(z)=B₀,v_(z)=v₀, v_(⊥)=0 and r=r₀. It emerges on the right hand side of thecusp 486 with r=r₀, B_(z)=−B₀, v_(⊥)=qB₀r₀/Mc and v_(z)=√{square rootover (v₀ ²−v_(⊥) ²)}

$\begin{matrix}{\frac{v_{z}}{v_{0}} = \sqrt{1 - \left( \frac{r_{0}\Omega_{0}}{v_{0}} \right)^{2}}} & (6)\end{matrix}$

where

$\Omega_{0} = \frac{{qB}_{0}}{Mc}$

is the cyclotron frequency. The rotation frequency of the ions is in arange of about 1-10 MHz, and preferably in a of about 5-10 MHz, which isthe frequency at which power generation takes place.

In order for the ions to pass through the cusp 486, the effective iongyro-radius must be greater than the width of the cusp 486 at the radiusr₀. It is quite feasible experimentally to reduce the axial velocity bya factor of 10 so that the residual axial energy will be reduced by afactor of 100. Then 99% of the ion energy will be converted torotational energy. The ion beam has a distribution of values for v₀ andr₀. However, because r₀ is proportional to v₀ as previously indicated bythe properties of the FRC based reactor, the conversion efficiency torotational energy tends to be 99% for all ions.

As depicted in FIG. 19B, the symmetrical electrode structure of the ICC420 of the present invention preferably includes four electrodes 494. Atank circuit (not shown) is connected to the electrode structures 494 sothat the instantaneous voltages and electric fields are as illustrated.The voltage and the tank circuit oscillate at a frequency of ω=Ω₀. Theazimuthal electric field E at the gaps 497 is illustrated in FIG. 19Band FIG. 22. FIG. 22 illustrates the electric field in the gaps 497between electrodes 494 and the field an ion experiences as it rotateswith angular velocity Ω₀. It is apparent that in a complete revolutionthe particle will experience alternately acceleration and decelerationin an order determined by the initial phase. In addition to theazimuthal electric field E_(θ) there is also a radial electric fieldE_(r). The azimuthal field E_(θ) is maximum in the gaps 497 anddecreases as the radius decreases. FIG. 22 assumes the particle rotatesmaintaining a constant radius. Because of the gradient in the electricfield the deceleration will always dominate over the acceleration. Theacceleration phase makes the ion radius increase so that when the ionnext encounters a decelerating electric field the ion radius will belarger. The deceleration phase will dominate independent of the initialphase of the ion because the radial gradient of the azimuthal electricfield E_(θ) is always positive. As a result, the energy conversionefficiency is not limited to 50% due to the initial phase problemassociated with conventional cyclotrons. The electric field E_(r) isalso important. It also oscillates and produces a net effect in theradial direction that returns the beam trajectory to the original radiuswith zero velocity in the plane perpendicular to the axis as in FIG.19C.

The process by which ions are always decelerated is similar to theprinciple of strong focusing that is an essential feature of modemaccelerators as described in U.S. Pat. No. 2,736,799. The combination ofa positive (focusing) and negative lens (defocusing) is positive if themagnetic field has a positive gradient. A strong focusing quadrupoledoublet lens is illustrated in FIG. 23. The first lens is focusing inthe x-direction and defocusing in the y-direction. The second lens issimilar with x and y properties interchanged. The magnetic fieldvanishes on the axis of symmetry and has a positive radial gradient. Thenet results for an ion beam passing through both lenses is focusing inall directions independent of the order of passage.

Similar results have been reported for a beam passing through a resonantcavity containing a strong axial magnetic field and operating in theTE₁₁₁ mode (see Yoshikawa et al.). This device is called a peniotron. Inthe TE₁₁₁ mode the resonant cavity has standing waves in which theelectric field has quadrupole symmetry. The results are qualitativelysimilar to some of the results described herein. There are quantitativedifferences in that the resonance cavity is much larger in size (10meter length), and operates at a much higher frequency (155 MHz) andmagnetic field (10 T). Energy extraction from the high frequency wavesrequires a rectenna. The energy spectrum of the beam reduces theefficiency of conversion. The existence of two kinds of ions is a moreserious problem, but the efficiency of conversion is adequate for aD-He³ reactor that produces 15 MeV protons.

A single particle orbit 422 for a particle within the ICC 420 isillustrated in FIG. 19C. This result was obtained by computer simulationand a similar result was obtained for the peniotron. An ion entering atsome radius r₀ spirals down the length of the ICC and after losing theinitial rotational energy converges to a point on a circle of the sameradius r₀. The initial conditions are asymmetric; the final statereflects this asymmetry, but it is independent of the initial phase sothat all particles are decelerated. The beam at the ion collector end ofthe ICC is again annular and of similar dimensions. The axial velocitywould be reduced by a factor of 10 and the density correspondinglyincreased. For a single particle an extracting efficiency of 99% isfeasible. However, various factors, such as perpendicular rotationalenergy of the annular beam before it enters the converter, may reducethis efficiency by about 5%. Electric power extraction would be at about1-10 MHz and preferably about 5-10 MHz, with additional reduction inconversion efficiency due to power conditioning to connect to a powergrid.

As shown in FIGS. 20A and 20B, alternative embodiments of the electrodestructures 494 in the ICC 420 may include two symmetrical semi-circularelectrodes and/or tapered electrodes 494 that taper towards the ioncollector 492.

Adjustments to the ion dynamics inside the main magnetic field of theICC 420 may be implemented using two auxiliary coil sets 500 and 510, asshown in FIGS. 24A and 24B. Both coil sets 500 and 510 involve adjacentconductors with oppositely directed currents, so the magnetic fieldshave a short range. A magnetic-field gradient, as schematicallyillustrated in FIG. 24A, will change the ion rotation frequency andphase. A multi-pole magnetic field, as schematically illustrated in FIG.24B, will produce bunching, as in a linear accelerator.

Reactor

FIG. 25 illustrates a 100 MW reactor. The generator cut away illustratesa fusion power core region having superconducting coils to apply auniform magnetic field and a flux coil for formation of a magnetic fieldwith field-reversed topology. Adjacent opposing ends of the fusion powercore region are ICC energy converters for direct conversion of thekinetic energy of the fusion products to electric power. The supportequipment for such a reactor is illustrated in FIG. 26.

Propulsion System

FIG. 27 illustrates a plasma-thrust propulsion system 800. The systemincludes a FRC power core 836 in which a fusion fuel core 835 iscontained and from both ends of which fusion products emerge in the formof an annular beam 837. An ICC energy converter 820 coupled to one endof the power core. A magnetic nozzle 850 is positioned adjacent theother end of the power core. The annular beam 837 of fusion productsstream from one end of the fusion power core along field lines into theICC for energy conversion and from the other end of the power core alongfield lines out of the nozzle for thrust T.

While the invention is susceptible to various modifications andalternative forms, a specific example thereof has been shown in thedrawings and is herein described in detail. It should be understood,however, that the invention is not to be limited to the particular formdisclosed, but to the contrary, the invention is to cover allmodifications, equivalents, and alternatives falling within the spiritand scope of the appended claims.

1. (canceled)
 2. The method of claim 7, further comprising the step ofapplying an oscillating potential to the plurality of electrodes.
 3. Themethod of claim 7, wherein the step of forming an electric fieldincludes creating an azimuthal electric field across the plurality ofgaps.
 4. The method of claim 7, further comprising the step ofdecelerating the ions.
 5. The method of claim 7, wherein the ions areinjected in the form an annular beam.
 6. The method of claim 5, furthercomprising the step of directing the annular beam through a magneticcusp.
 7. A method of converting fusion product energies into electricenergy, comprising the steps of injecting ions along a helical pathwithin a generally cylindrical cavity formed of a plurality ofsemi-cylindrical electrodes in spaced relation with one another forminga plurality of elongate gaps there between, wherein the ions areinjected in the form an annular beam, converting substantially all ofthe injected ions' axial energy to rotational energy, forming amulti-pole electric field within the cavity, the electric fieldcomprising three or more poles, converting at least a portion of the ionenergy into electrical energy, and collecting charge neutralizingelectrons from the annular beam as the electrons follow magnetic fieldlines of a magnetic cusp.
 8. The method of claim 7 further comprisingthe step of collecting the ions once a substantial portion of theirenergy is converted to electric energy.
 9. The method of claim 7 furthercomprising the step of conditioning the electric energy converted fromthe ion energy to match existing power grids.
 10. The method of claim 7wherein the plurality of electrodes comprises at least four electrodes.11. (canceled)
 12. A method of converting fusion product energies intoelectric energy, comprising the steps of injecting ions along a helicalpath within a generally cylindrical cavity formed of a plurality ofsemi-cylindrical electrodes in spaced relation with one another forminga plurality of elongate gaps there between, converting substantially allof the injected ions' axial energy to rotational energy, forming amulti-pole electric field within the cavity, the electric fieldcomprising three or more poles, converting at least a portion of the ionenergy into electrical energy, and creating a magnetic cusp, wherein thestep of creating the magnetic cusp comprises the steps of creating firstand second magnetic fields within the cavity, wherein field lines of thefirst and second magnetic fields extend in opposing directions, andjoining the first and second magnetic fields.
 13. (canceled)
 14. Themethod of claim 20, further comprising the step of applying anoscillating potential to the three or more electrodes.
 15. The method ofclaim 20, further comprising the step of creating an azimuthal electricfield across each of the gaps.
 16. The method of claim 20, furthercomprising the step of decelerating the ions.
 17. The method of claim20, wherein the injecting step includes converting substantially all ofthe ions axial energy to rotational energy.
 18. (canceled)
 19. Themethod of claim 20, further comprising the step of directing the annularbeam through a magnetic cusp.
 20. A method of converting fusion productenergies into electric power, comprising the steps of injecting ionsalong a helical path within a cylindrical cavity formed by three or moreelongate electrodes in spaced relation with an elongate gap formedbetween adjacent electrodes of the three or more electrodes, wherein theions are injected in the form an annular beam, converting at least aportion of the ion energy into electrical energy, and collecting chargeneutralizing electrons from the annular beam as the electrons followmagnetic field lines of a magnetic cusp.
 21. The method of claim 20further comprising the step of collecting the ions once a substantialportion of their energy is converted to electric energy.
 22. The methodof claim 21 further comprising the step of conditioning the electricenergy converted from the ion energy to match existing power grids. 23.(canceled)
 24. A method of converting fusion product energies intoelectric power, comprising the steps of injecting ions along a helicalpath within a cylindrical cavity formed by three or more elongateelectrodes in spaced relation with an elongate gap formed betweenadjacent electrodes of the three or more electrodes, converting at leasta portion of the ion energy into electrical energy, and creating amagnetic cusp, wherein the step of creating the magnetic cusp comprisesthe steps of creating first and second magnetic fields within thecavity, wherein field lines of the first and second magnetic fieldsextend in opposing directions, and joining the first and second magneticfields.
 25. (canceled)
 26. The method of claim 30, further comprisingthe step of applying an oscillating potential to the three or moreelectrodes.
 27. The method of claim 30, further comprising the step ofcreating azimuthal electric fields across the gaps.
 28. The method ofclaim 27, further comprising the step of decelerating the ions.
 29. Themethod of claim 30, wherein the injecting step includes convertingsubstantially all of the ions' axial energy to rotational energy. 30.(canceled)
 31. (canceled)
 32. (canceled)
 33. (canceled)
 34. The methodof claim 41, further comprising the step of applying an oscillatingpotential to three or more elongate electrodes in spaced relation withelongate gaps formed between adjacent electrodes, the three or moreelongate electrodes forming a cylindrical cavity.
 35. The method ofclaim 41, wherein the step of creating a multi-pole elongate electricfield includes creating azimuthal electric fields across elongate gapsformed between three or more electrodes forming a cylindrical cavity.36. (canceled)
 37. (canceled)
 38. The method of claim 41, furthercomprising the step of directing the annular beam through the magneticcusp.
 39. The method of claim 41, further comprising the step ofdecelerating the ions.
 40. The method of claim 41, wherein the injectingstep includes converting substantially all of the ions' axial energy torotational energy.
 41. A method of converting fusion product energiesinto electric power, comprising the steps of creating a multi-poleelongate electric field comprising three or more poles, creating firstand second magnetic fields within the cavity, wherein unidirectionalfield lines of the first and second magnetic fields extend in opposingdirections, joining the field lines of the first and second magneticfields to form a magnetic cusp, injecting ions in the form of an annularbeam along a helical path through the electric field, converting atleast a portion of the ion energy into electrical energy, and collectingcharge neutralizing electrons from the annular beam as the electronsfollow magnetic field lines of the magnetic cusp.
 42. The method ofclaim 41 further comprising the step of collecting the ions once asubstantial portion of their energy is converted to electric energy. 43.The method of claim 42 further comprising the step of conditioning theelectric energy converted from the ion energy to match existing powergrids.